@article{15506dfa8001497ba94cc3f4506a863b,

title = "Entanglement and its relation to energy variance for local one-dimensional Hamiltonians",

abstract = "We explore the relation between the entanglement of a pure state and its energy variance for a local one-dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state of arbitrarily small energy variance δ2 for N spins, with bond dimension scaling as ND01/δ, where D0>1 is a constant. This implies that a polynomially increasing bond dimension is enough to construct states with energy variance that vanishes with the inverse of the logarithm of the system size. We run numerical simulations to probe the construction on two different models and compare the local reduced density matrices of the resulting states to the corresponding thermal equilibrium. Our results suggest that the spatially homogeneous states with logarithmically decreasing variance, which can be constructed efficiently, do converge to the thermal equilibrium in the thermodynamic limit, while the same is not true if the variance remains constant.",

author = "Ba{\~n}uls, {Mari Carmen} and Huse, {David A.} and Cirac, {J. Ignacio}",

note = "Funding Information: We are thankful to A. Dymarsky for discussions. This work was partly supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy-EXC-2111-390814868, and by the European Union through the ERC grant QUENOCOBA, ERC-2016-ADG (Grant No. 742102). M.C.B. acknowledges the hospitality of KITP, where part of this work was developed, and support from the National Science Foundation under Grant No. NSF PHY-1748958. D.A.H. was supported in part by DOE Office of Science Grant No. DE-SC0016244. Funding Information: We are thankful to A. Dymarsky for discussions. This work was partly supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy—EXC-2111—390814868, and by the European Union through the ERC grant QUENOCOBA, ERC-2016-ADG (Grant No. 742102). M.C.B. acknowledges the hospitality of KITP, where part of this work was developed, and support from the National Science Foundation under Grant No. NSF PHY-1748958. D.A.H. was supported in part by DOE Office of Science Grant No. DE-SC0016244. Publisher Copyright: {\textcopyright} 2020 authors. Published by the American Physical Society.",

year = "2020",

month = apr,

day = "1",

doi = "10.1103/PhysRevB.101.144305",

language = "English (US)",

volume = "101",

journal = "Physical Review B",

issn = "2469-9950",

publisher = "American Physical Society",

number = "14",

}